The PHSELECT Procedure

Note: Input data must be in a CAS table that is accessible in your CAS session. You must refer to this table by using a two-level name. The first level must be a CAS engine libref, and the second level must be the table name. For more information, see the sections Using CAS Sessions and CAS Engine Librefs and Loading a SAS Data Set onto a CAS Server in Chapter 2, Shared Concepts.

The following DATA step creates the data table mycas.getStarted in your CAS session. This data table consists of 100 observations on a failure time variable (Time), an indicator variable (Status) that has two values (0 for censored observations and 1 for event observations), three classification variables (C1–C3), and four continuous variables (X1–X4). This DATA step assumes that your CAS engine libref is named mycas, but you can substitute any appropriately defined CAS engine libref.

data mycas.getStarted;
   input Time Status C1$ C2 C3$ X1-X4;
   datalines;
   53       0      Low          1    M     1.11    2.000    3.6128    12.0
   12       0      High         1    M     1.40    1.362    3.8388     8.8
   11       1      Low          1    F     1.57    1.672    3.8865     7.5
    7       1      Medium       0    M     1.04    2.000    3.7324     5.1
    2       1      Low          1    M     1.52    2.000    3.8751     9.8
   41       0      High         1    M     1.76    1.447    3.7243    12.8
    6       1      Critical     1    F     1.36    1.462    3.5441     9.0
    6       1      Critical     1    M     1.42    1.690    3.9294    10.4
   16       1      Medium       1    M     1.32    0.699    3.6990     8.8
   41       1      Medium       1    M     1.00    1.477    3.4771    10.2
    2       1      High         0    M     1.30    2.000    3.7243     5.1
   58       1      Medium       1    M     1.20    1.580    3.6990    12.1
   11       1      High         1    M     1.08    1.903    3.5051     9.6
   12       0      Critical     1    F     1.15    1.146    3.6435    11.6
   16       0      High         1    F     1.15    0.903    3.8573    13.0
   54       1      Medium       1    M     1.26    1.699    3.7243     9.0
   51       1      Low          0    M     1.57    1.041    3.4150     7.7
   67       1      Medium       1    M     1.32    1.041    3.6435    12.8
    1       1      Low          1    M     1.94    1.954    3.9868    12.0
   19       0      Medium       1    M     1.32    2.000    3.7709    13.0
    1       1      Medium       1    M     2.22    1.954    3.6628     9.4
   35       1      Medium       0    M     1.11    1.176    3.6532     7.0
   41       1      High         1    M     1.15    1.342    3.5185     5.0
   58       1      Medium       1    M     1.20    1.580    3.6990    12.1
   11       1      Medium       1    M     1.11    1.279    3.8808    14.0
   41       1      Medium       1    M     1.00    1.477    3.4771    10.2
   19       1      High         0    M     1.26    1.929    3.7924     7.5
   89       1      High         1    M     1.32    1.623    3.6532    14.0
    4       0      Medium       1    F     1.95    0.778    4.0453    10.2
    6       1      Critical     1    F     1.36    1.462    3.5441     9.0
   57       0      Low          1    F     1.26    1.954    3.9685    12.5
    5       1      High         1    M     2.24    1.663    4.9542    10.1
   17       1      Medium       1    F     1.59    1.613    3.4314    11.2
   77       0      Low          1    F     1.08    0.954    3.6812    14.0
   66       1      High         1    M     1.45    1.820    3.7853     6.6
   16       1      Medium       1    M     1.32    0.699    3.6990     8.8
    8       0      Critical     1    M     1.08    1.653    3.8325     9.9
   19       1      High         0    M     1.26    1.929    3.7924     7.5
   37       1      High         1    F     1.60    1.204    3.9542    11.0
   52       1      Medium       1    M     1.00    1.653    3.8573    10.1
   13       0      High         0    F     1.66    1.792    3.6435     4.9
    3       1      Medium       1    F     1.54    1.935    4.4757     6.7
   51       1      Low          0    M     1.57    1.041    3.4150     7.7
    2       1      High         0    M     1.30    2.000    3.7243     5.1
   25       1      Medium       1    M     1.00    1.644    3.8195    12.4
   11       1      Low          1    F     1.57    1.672    3.8865     7.5
   19       1      Low          1    M     1.08    2.000    3.9191    14.4
    9       1      Low          1    M     1.72    1.740    3.7993     8.2
    6       1      Medium       1    M     1.11    1.398    3.5185     9.7
   16       1      Medium       1    M     1.34    2.000    3.9345     9.0
   12       0      High         1    M     1.40    1.362    3.8388     8.8
   17       1      High         1    M     1.23    1.447    3.8808    10.0
   17       1      High         1    M     1.23    1.447    3.8808    10.0
   41       0      High         1    M     1.76    1.447    3.7243    12.8
   88       1      High         1    F     1.18    1.756    3.5563    10.6
   16       0      High         1    F     1.15    0.903    3.8573    13.0
    4       0      Low          1    F     1.92    1.623    3.9590    10.0
    7       1      Low          1    M     1.18    1.519    3.7243    11.4
   19       0      Medium       1    M     1.32    1.519    3.8808    10.8
    8       0      Critical     1    M     1.08    1.653    3.8325     9.9
   57       0      Low          1    F     1.26    1.954    3.9685    12.5
    7       1      Medium       1    M     1.98    1.568    3.3617     9.5
   19       1      Low          1    M     1.08    2.000    3.9191    14.4
    7       0      Low          1    F     1.53    1.881    3.5911    10.2
    5       1      High         1    F     1.68    1.732    3.7324     6.5
    2       1      Low          0    M     1.75    1.255    3.8062    11.3
    1       1      Low          1    M     1.94    1.954    3.9868    12.0
   15       1      Low          1    M     1.60    1.431    3.6902    10.6
   26       1      Low          1    M     1.23    2.000    3.6021    11.2
   92       1      Low          1    M     1.43    1.415    4.0755    11.0
   11       1      Medium       1    M     1.30    1.820    3.7993    13.2
    3       1      Medium       1    F     1.54    1.935    4.4757     6.7
   66       1      High         1    M     1.45    1.820    3.7853     6.6
    1       1      Medium       1    M     2.22    1.954    3.6628     9.4
   11       1      Medium       1    M     1.30    1.820    3.7993    13.2
   14       1      Medium       1    M     1.40    1.255    3.7243    14.6
   32       1      High         1    M     1.32    1.634    3.6990    10.6
   24       1      High         1    M     1.30    0.477    4.0899    14.6
   18       1      Critical     1    F     1.45    0.903    3.5682     7.5
    5       1      High         1    F     1.68    1.732    3.7324     6.5
    2       1      Low          0    M     1.75    1.255    3.8062    11.3
   26       1      Low          1    M     1.23    2.000    3.6021    11.2
   11       1      High         1    M     1.23    1.176    3.7709    12.0
   28       0      High         1    M     1.23    1.672    3.7482     7.3
   19       0      Medium       1    M     1.32    2.000    3.7709    13.0
   54       1      Medium       1    M     1.26    1.699    3.7243     9.0
    2       1      Low          1    M     1.52    2.000    3.8751     9.8
    7       0      Medium       1    M     1.11    1.857    3.7993    12.4
   19       0      Medium       1    M     1.32    1.519    3.8808    10.8
    6       1      Critical     1    M     1.42    1.690    3.9294    10.4
    6       1      Medium       1    M     1.11    1.398    3.5185     9.7
   11       1      Medium       1    M     1.11    1.279    3.8808    14.0
    6       1      Critical     0    M     2.11    1.362    3.5441    10.2
   13       1      Medium       0    M     0.78    1.398    3.5798     5.5
   18       1      Critical     1    F     1.45    0.903    3.5682     7.5
    7       0      Low          1    F     1.53    1.881    3.5911    10.2
   53       0      Low          1    M     1.11    2.000    3.6128    12.0
   11       1      High         1    M     1.08    1.903    3.5051     9.6
   11       0      High         1    M     1.61    1.845    3.7324    14.0
   89       1      High         1    M     1.32    1.623    3.6532    14.0
;

The following statements fit a Cox proportional hazards model to these data by using three classification effects for the variables C1–C3 and four regressor effects for the variables X1–X4. The ITHIST option displays a table that summarizes the steps of the optimization.

proc phselect data=mycas.getStarted ithist;
   class C1-C3;
   model Time*Status(0) = C1-C3 X1-X4;
run;

The output from this analysis is presented in Figure 1 through Figure 8.

Figure 1 displays the "Model Information" table. The variable Time is the failure time variable. The variable Status is the censoring variable; the value 0 indicates censored observations. The PHSELECT procedure uses a quasi-Newton algorithm to maximize the partial likelihood to estimate the regression coefficients.

Figure 2 displays the "Number of Observations" table. All 100 observations in the data table are used in the analysis; of them, 26 are censored and 74 are uncensored.

The classification variables C1–C3 are parameterized using the GLM parameterization, which is the default. The variable C1 has four unique formatted levels; each of the two variables C2 and C3 has two levels. The classification levels are displayed in the "Class Level Information" table in Figure 3.

The "Iteration History" table is shown in Figure 4. The quasi-Newton algorithm converged after 12 iterations, not counting the initial setup iteration.

Figure 5 displays the final convergence status of the quasi-Newton algorithm. The GCONV=1E-8 convergence criterion is satisfied.

Figure 6 displays the "Dimensions" table for this model. This table summarizes some important sizes of various model components. For example, it shows that the design matrix has 12 columns: 4 columns for the effects that are associated with the classification variable C1, 2 columns for each of the classification variables C2 and C3, and 1 column for each of the continuous variables X1–X4. However, the rank of the crossproducts matrix is only 9. Because the classification variables C1–C3 use GLM parameterization, there is one singularity in the crossproducts matrix of the model for each classification variable. Consequently, only nine parameters enter the optimization.

The "Fit Statistics" table is shown in Figure 7. The –2 log likelihood at the converged estimates is 510.78672. You can use this value to compare the model to nested model alternatives by means of a likelihood ratio test. To compare models that are not nested, you can use information criteria such as Akaike’s information criterion (AIC), Akaike’s bias-corrected information criterion (AICC), and the Schwarz Bayesian information criterion (BIC). These criteria penalize the –2 log partial likelihood for the number of parameters.

The "Parameter Estimates" table in Figure 8 shows that many parameters have fairly large p-values, indicating that one or more of the model effects might not be necessary.

Finally, the procedure displays the table in Figure 9, which shows the amount of time (in seconds) that PROC PHSELECT required to perform different tasks in the analysis.